My experience with barcode scanners is fairly limited, but anything that is a standard usb scanner has always outputted whatever was scanned as if it was typed by a keyboard.

Any of the scanners I have used (only a few) were able to be configured to to automatically add a control character after the result of the scan, e.g. Enter, Tab, Space, New Line etc etc

What I did for one web interface was use JavaScript to put the focus in a field on the page automatically, when you scanned it was configured to send the Return/Enter character and submit the form. Validated the barcode saved the data and reloaded the page with the form and the focus once again on the input field.

Let's say I want "Enter" to be the control character. How or where do I set it? Is it done physically on scanner or in it's software? I am not sure if they come with software though, or maybe they are PnP. Just guessing.

It would be something you configured on the scanner. The ones I've used have both had software you could use, or their manuals had pages of barcodes you could scan to set the scanner up to do particular tasks.